By David H. West and Gregory Yablonsky (Eds.)
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Extra resources for Advances in Chemical Engineering
It is clear that by replacing all variables in the integrals of the form Z X 0 i ! kir # xj j j d by constant constraints (10) reduce to linear inequalities xr X i ! kir # xj j j d ð52Þ and their inclusion into MEIS does not affect the reducibility of the latter to the CP problems. Unfortunately it is not always possible to use only linear inequalities. In further studies we will have to include into the kinetic constraints both the equations of nonlinear chemical kinetics and the nonlinear equations of transfer processes.
The minimized economic characteristic of the network as a whole, prove to be nonadditive, which does not allow the use of dynamic programming. , 1992; Sumaro kov, 1976). According to this method motion to the minimum point of the economic functional F(x, Pbr) is performed alternately along the concave (F(x)) and convex (F(Pbr)) directions. The convex problem is solved by the dynamic programming method and the concave one reduces to calcula tion of flow distribution. The pressure losses in this case are optimized on the tree obtained as a result of assumed flow shutoff at the end points of some branches.
Construction of the flow models of the second group (with conditional flows) will be exemplified by the MEIS of chemical system with constant T, P, and y that has the form: find 2 max4FxððÞÞ ¼ X 3 � � �� cj xj ðÞ5 ¼ F x ext ð29Þ j2J ext subject to xj ¼ yj þ X ij i ; j ¼ 1; … ; n; i ¼ 1; … ; m; ð30Þ i Dt ðyÞ ¼ f : xðÞ yg; ð31Þ jr ðxr ðÞ; zr Þ cr ; r; 2 Rlim ; ð32Þ GðxðÞÞ ¼ X Gj ðxðÞÞxj ; ð33Þ j xj ! 0; 0 i 1; ð34Þ where = (1,…,m)T; i —the degree of completeness (a coordinate) of the i-th reaction; —a stoichiometric coefficient.